The MPEG (Moving Picture Experts Group) and the VCEG (Video Coding Experts Group) have developed a new video compression standard entitled AVC (Advanced Video Coding). This standard offers the capacity of video compression greater than the previous standards.The motion estimation which is a phase of the video compression is extremely computer-intensive and therefore demands most of the processing time. When Full Search [1] method is used for H.264/AVC, this process is extremely expensive. In order to reduce encoding time, the reference software JM (throughout this work, JM98 is the version used) has respectively adopted a fast motion estimation method for the integer pixel called UMHexagonS and a method for the sub- pixel called CBFPS. A method proposed by Xiaoquan Yi, Jun Zhang, Nam Ling e Weijia Shang [2] called here P021 (as referenced by the Joint Video Team) has shown, when compared to the reference software JM, a simple way of motion estimation that increases the speed of coding process while maintaining the video visual quality. In order to decrease the processing time and computational cost of these methods, which are: i) particularly needed in mobile video coding applications such as mobile phones and palmtops; ii) in real time applications such as videoconference, this work proposes a motion estimation method that eliminates the processing of blocks that does not produce benefits for the half-pixel search. The simulation results show that the proposed method reduces the processing time in 76,17%, 75,95% and 11,74% in average when respectively compared with Full Search, JM98 and P021 methods, without relevant impact in video quality. Besides, this method produces a bits rate increase of 8,72% , 8,06% e 8,02% in average when compared with the same methods. This is in our opinion, an inexpensive price to be paid when the time benefits are considered.